Weak Solutions for the Vlasov-Poisson Initial-Boundary Value Problem with Bounded Electric Field

Bostan, Mihaï

doi:10.1007/s11401-005-0448-6

Cited by 5 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[2,14,4]. Following the arguments in [4], leads to a L ∞ estimate for the electric field, and therefore, if the initial density f in is smooth, with compact support, then so is the restriction of…”

Section: Convergence Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The Effective Vlasov--Poisson System for the Finite Larmor Radius Regime

Bostan¹,

Finot²

2016

Multiscale Model. Simul.

View full text Add to dashboard Cite

The subject matter of this paper concerns the finite Larmor radius regime of the Vlasov-Poisson system for strongly magnetized plasmas. We appeal to gyro-average methods, and determine the explicit expressions for the velocity and acceleration fields in the limit Vlasov equation. We investigate the Hamiltonian structure of the limit model (trajectories), analyse its properties (conservations of the mass, kinetic energy, electric energy) and justify rigorously the asymptotic behavior, following the formal arguments developed in 1 .

show abstract

Section: Convergence Resultsmentioning

confidence: 99%

“…The well posedness of the Vlasov-Poisson system follows by standard arguments, based on uniform mass and energy estimates, with respect to ε > 0, see [2,4]. The asymptotic behavior comes by performing a two scale analysis.…”

mentioning

confidence: 99%

The Effective Vlasov--Poisson System for the Finite Larmor Radius Regime

Bostan¹,

Finot²

2016

Multiscale Model. Simul.

View full text Add to dashboard Cite

show abstract

“…Actually following the ideas in [4] it is possible to obtain more uniform bounds with respect to the parameter ε. For any R > 0 we can write…”

Section: Uniform Estimatesmentioning

confidence: 99%

The Vlasov–Poisson system with strong external magnetic field. Finite Larmor radius regime

Bostan

2009

Asymptotic Analysis

Self Cite

View full text Add to dashboard Cite

We study here the finite Larmor radius regime for the Vlasov-Poisson equations with strong external magnetic field. The derivation of the limit model follows by formal expansion in power series with respect to a small parameter. If we replace the particle distribution by the center distribution of the Larmor circles the limit of these densities satisfies a transport equation, whose velocity is given by the gyro-average of the electric field. We justify rigorously the convergence towards the above model and we investigate the well-posedness of it.

show abstract